I left a piece of me in a piece I gave you

Iggy is using the metaphor of the Rolex watch she gave as a gift to Rocky as giving investments of herself — whether they be her affection, body, or more specifically in this case, her time, which she has evidently pointed out is more valuable than anything.

By giving him this piece of her, he now holds that and forever will. She will never get that time back that she gave him, because time is intangible, unlike the physicality of the watch.